You're right. I feel pretty silly having asked the question now. I did a little more digging and I found a site where I can put in questions like this and get immediate feedback without wasting other people's time or feeding the ego's of elitist technocrats. I just typed this question there just now and was provided a listing of numerous sites with well-developed ideas and thorough explanations. You just gave me a large portion of my life back. Thanks!
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Ian FeltonJul 12 '11 at 4:46

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The point of directing you to the existing tag isn't to be disparaging or "technocratic" or say that you're wasting time. It's to make it easy to find what are essentially direct, already-there-for-you answers to your question. That, in addition to the answers given below, should be immediately helpful to you or to anyone else who comes along later. I'm not sure that really warrants the tone of your response.
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mattdmJul 12 '11 at 5:11

Apart from rules of thumb like the rule of thirds, there are mand general compositional principles which are generally the same in all art forms, things such as balance, space, pattern, texture, lines and shapes, light and shadow.

Very common compositional techniques in photography that I can think of

leading lines - leading the viewer's eye through the image

patterns, and I think even more importantly broken/interrupted patterns

selective focus or color (attracting attention to the subject by blurring/desaturating the background, I guess vignettes fall into this category

negative space

unusual perspectives - images of objects from a viewpoint not usually seen (ant's eye view of a flower or pet), extreme wide angle or tele shots

framing - leaving space in front of the subject if moving, or looking out of the picture

with wide angle images, having strong foreground interest

use of strong contrast, bright objects or bright colors to draw the viewer's eye

lines - diagonal lines and curves are more "dynamic", while vertical ines imply strenght and horizontal lines are more static and calming

horizon - generally should not be placed in the center of the image, either the foreground or sky should be given more space - one exception would be water reflections where dead center often works

in general the main subject should be off centre (rule of thirds or otherwise) but usually needs balancing by other objects

triangles generally make for strong compositions

I think the best images are ones the attract the eye even when looking at a small thumbnail, and you're not sure what the subject is, but the eye is attracted by a strong pattern, shape or color.

The article below is worth a read. It covers a lot of the above, and more.

For interesting ways to break a rule, learn why the rule works and break it when you want to achieve opposite effect. For example, break the rule of odds when you want to stress symmetry and dullness of a scene.